2d:null 2e:["$","title",null,{"children":"stdlib: Real-time k-means clustering | Athan | Observable"}] 33:Tab1,/** * Returns a iterator protocol-compliant object for simulating a discrete-time hidden Markov chain. * * @param {integer} N - number of data points to simulate * @param {ArrayLikeObject} initial - initial probabilities * @param {ArrayLikeObject} transition - transition probabilities * @param {ArrayLikeObject} means - state observation means * @param {ArrayLikeObject} sigmas - state observation standard deviations * @param {integer} [seed] - pseudorandom number generator (PRNG) seed * @returns {Iterator} iterator */ function simulator( N, initial, transition, means, sigmas, seed ) { var nStates; var state; var probs; var iter; var rand; var FLG; var n; var i; nStates = initial.length; n = -1; // Define a PRNG seed: seed = seed || (randi()>>>0); // Create a seeded PRNG: rand = randu.factory({ 'seed': seed }); // Convert the initial probabilities to cumulative probabilities: initial = csum( initial ); // Convert each set of transition probabilities to cumulative probabilities: transition = transition.slice(); // avoid mutation for ( i = 0; i < nStates; i++ ) { transition[ i ] = csum( transition[ i ] ); } // Return an iterator protocol-compliant object: iter = {}; iter.next = next; iter.return = end; return iter; /** * Generates the next simulated observation. * * @private * @returns {Object} simulated observation as an iterator protocol-compliant object */ function next() { var r; var v; var i; n += 1; if ( FLG || n >= N ) { return { 'done': true }; } if ( n === 0 ) { // Determine the initial state: r = rand(); for ( i = 0; i < nStates; i++ ) { if ( r < initial[ i ] ) { state = i; v = corrupt( means[ state ], sigmas[ state ] ); v.push( state ); return { 'value': v, 'done': false }; } } } else { // Simulate the next state: probs = transition[ state ]; r = rand(); for ( i = 0; i < nStates; i++ ) { if ( r < probs[ i ] ) { state = i; v = corrupt( means[ state ], sigmas[ state ] ); v.push( state ); return { 'value': v, 'done': false }; } } } } /** * Finishes the iterator. * * @private * @param {*} [value] - value to return * @returns {Object} iterator protocol-compliant object */ function end( value ) { FLG = true; if ( arguments.length ) { return { 'value': value, 'done': true }; } return { 'done': true }; } }34:T481,cluster_data = { var states; var seed; var vec; var res; var it; var cx; var cy; var x; var y; var v; var i; // Define a seed in order to ensure that simulated data is easily reproducible: seed = 123456; // Create a new (seeded) simulator: it = simulator( N, I, A, means, sigmas, seed ); x = []; y = []; states = []; cx = []; cy = []; vec = vector( [ 0.0, 0.0 ] ); // Simulate each observation individually and incrementally update the k-means accumulator... while ( true ) { v = it.next(); if ( v.done ) { break; } // Note: we assume 2-dimensional data... x.push( v.value[ 0 ] ); vec.set( 0, v.value[ 0 ] ); y.push( v.value[ 1 ] ); vec.set( 1, v.value[ 1 ] ); states.push( v.value[ 2 ] ); // Update the accumulator: res = cluster( vec ); // If results are returned, store the centroid positions... if ( res ) { for ( i = 0; i < nStates; i++ ) { cx.push( res.centroids.get( i, 0 ) ); cy.push( res.centroids.get( i, 1 ) ); } } } return [ [ x, cx ], [ y, cy ], states, res ]; }35:Tceb,Analyzer = { /** * Analyzer constructor. * * @returns {Analyzer} Analyzer instance */ function Analyzer() { this.init(); return this; } /** * Initializes an analyzer. */ Analyzer.prototype.init = function init() { // Initialize `x` and `y` data vectors: this.x = new Float64Array( N ); this.y = new Float64Array( N ); // Initialize centroid data vectors: this.cx = new Float64Array( nStates ); this.cy = new Float64Array( nStates ); // Initialize a "time" vector: this.t = new Uint32Array( N ); // Initialize a "time" counter: this.i = -1; // Initialize a vector for updating the k-means accumulator: this.v = vector( [ 0.0, 0.0 ] ); // Initialize a k-means accumulator: this.acc = incrkmeans( nStates, ndims, { 'metric': 'euclidean', 'init': [ 'kmeans++' ], 'seed': 1234 // provide seed in order to ensure reproducible k-means++ initialization }); // Initialize a plot constructor for visualizing simulated timeseries: this.timeseries = plot({ 'title': 'Simulated Timeseries', 'xMin': 0, 'xMax': 250, 'yMin': -0.1, 'yMax': 1.1, 'width': 800, 'height': 600 }); // Initialize a plot constructor for a two-dimensional scatter plot: this.scatter = plot({ 'title': 'Cluster Analysis', 'xMin': -0.1, 'xMax': 1.1, 'yMin': -0.1, 'yMax': 1.1, 'lineStyle': 'none', 'symbols': 'closed-circle', 'symbolsOpacity': [ 0.15, 1.0 ], 'width': 600, 'height': 600 }); }; /** * Updates an analyzer. * * @param {ArrayLikeObject} datum - datum * @returns {Analyzer} Analyzer instance */ Analyzer.prototype.update = function update( datum ) { var res; var i; // Update the "time" counter: this.i += 1; // Update the "time" vector: this.t[ this.i ] = this.i; // Cache the provided data: this.x[ this.i ] = datum[ 0 ]; this.y[ this.i ] = datum[ 1 ]; // Update the accumulator: this.v.set( 0, datum[ 0 ] ); this.v.set( 1, datum[ 1 ] ); res = this.acc( this.v ); // If results are returned, update the centroid positions... if ( res ) { for ( i = 0; i < nStates; i++ ) { this.cx[ i ] = res.centroids.get( i, 0 ); this.cy[ i ] = res.centroids.get( i, 1 ); } } return this; }; /** * Renders analysis plots. * * @returns {Array} plots */ Analyzer.prototype.render = function render() { var t; var x; var y; // Create typed array views: t = new Uint32Array( this.t.buffer, 0, this.i+1 ); x = new Float64Array( this.x.buffer, 0, this.i+1 ); y = new Float64Array( this.y.buffer, 0, this.i+1 ); // Update the timeseries plot: this.timeseries.x = [ t, t ]; this.timeseries.y = [ x, y ]; if ( this.i > 250 ) { this.timeseries.xMin = t[ this.i-250 ]; this.timeseries.xMax = t[ this.i ]; } // Update the scatter plot: this.scatter.x = [ x, this.cx ]; this.scatter.y = [ y, this.cy ]; // Render the plots: return [ this.timeseries.render( 'html' ), this.scatter.render( 'html' ) ]; } return Analyzer; }36:[] 31:{"id":"de9012ed3fcb78ac","slug":"stdlib-real-time-k-means-clustering","title":"stdlib: Real-time k-means clustering","thumbnail":"88442649b4d74f0979dbcdcbd3bb64388f1c25fddc227792823dee8a76240371","access_level":"public","create_time":"$D2018-11-22T22:29:09.237Z","update_time":"$D2025-03-15T05:30:13.419Z","view_time":null,"first_public_time":"$D2018-12-04T17:53:23.236Z","has_unpublished_edits":null,"fork":false,"stars":18,"starred":false,"owner":{"type":"team","id":"305fcf2f11e07649","login":"kgryte","name":"Athan","avatar_url":"https://avatars-next.observableusercontent.com/62abcb0f1a226f03a1138db7fec8a58afd71e37ca89254954af372e75fb90a73","tier":"starter_2024"},"version":623,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"7b908ca3d7dc4524","login":"kgryte","name":"Athan","avatar_url":"https://avatars-next.observableusercontent.com/62abcb0f1a226f03a1138db7fec8a58afd71e37ca89254954af372e75fb90a73","tier":null}],"members":[{"type":"individual","id":"7b908ca3d7dc4524","login":"kgryte","name":"Athan","avatar_url":"https://avatars-next.observableusercontent.com/62abcb0f1a226f03a1138db7fec8a58afd71e37ca89254954af372e75fb90a73","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":7,"collection":{"id":"16cb696d0295f5bd","slug":"stdlib","title":"stdlib","owner":{"id":"305fcf2f11e07649","login":"kgryte","name":"Athan"}},"type":"notebook","body":{"title":"stdlib: Real-time k-means clustering","cells":[{"id":0,"value":"md`# stdlib: Real-time k-means clustering`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":239,"value":"md`\n**Note**: this notebook uses simulated data as we have control over data generation and are able to know the true underlying state of the simulated system.\n\nThe analytical approach can be readily applied to real data. \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":243,"value":"md`\n* * *\n\n## Getting Started\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":315,"value":"md`\nWe begin by loading various packages from [stdlib](https://github.com/stdlib-js/stdlib), a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing applications.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":246,"value":"md`\nFirst, we'll load various [pseudorandom number generators](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/random/base) used during data simulation\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":43,"value":"randi = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randi@umd/browser.js' )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"randu = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@umd/browser.js' )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"randn = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-normal@umd/browser.js' )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":249,"value":"md`\nThen, we load an API for creating [n-dimensional data structures](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/ndarray/ctor) for efficient vector and matrix operations and define convenience functions for creating vectors and matrices\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"ndarray = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/ndarray-ctor@umd/browser.js' )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":131,"value":"/**\n* Creates a vector from an array-like object.\n*\n* @param {ArrayLikeObject} x - source array\n* @returns {ndarray} vector\n*/\nfunction vector( x ) {\n return new ndarray( 'float64', new Float64Array( x ), [ x.length ], [ 1 ], 0, 'row-major' );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":204,"value":"/**\n* Converts a vector to a matrix.\n*\n* @param {ndarray} v - vector\n* @returns {ndarray} matrix\n*/\nfunction vec2mat( v ) {\n return new ndarray( 'float64', v.data, [ 1, 2 ], [ 2, 1 ], 0, 'row-major' );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":252,"value":"md`\nNext, we'll load the stdlib [plot](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/plot) API\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"plot_pkg = require( 'https://cdn.jsdelivr.net/npm/@stdlib/dist-plot-flat' )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":616,"value":"plot = plot_pkg.plot","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":255,"value":"md`\nAnd, finally, we'll load an accumulator for incrementally performing [k-means clustering](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/ml/incr/kmeans)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"incrkmeans = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/ml-incr-kmeans@umd/browser.js' )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":258,"value":"md`\n* * *\n\n## Simulation\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":261,"value":"md`\nIn order to generate synthetic 2-dimensional datasets, we'll define various simulation functions. The first is a function to compute the cumulative sum\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"/**\n* Computes the cumulative sum.\n*\n* @param {ArrayLikeObject} arr - array over which to compute the cumulative sum\n* @returns {Array} cumulative sum\n*/\nfunction csum( arr ) {\n var out;\n var i;\n \n out = [];\n out.push( arr[ 0 ] );\n for ( i = 1; i < arr.length; i++ ) {\n out.push( out[ i-1 ] + arr[ i ] );\n }\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":326,"value":"md`\nNext, we define a function for \"corrupting\" a signal by introducing Guassian noise\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"/**\n* Generates a \"corrupted\" (i.e., noisy) observation.\n*\n* @param {ArrayLikeObject} means - state observation means\n* @param {ArrayLikeObject} sigmas - state observation standard deviations\n* @returns {Array} noisy data\n*/\nfunction corrupt( means, sigmas ) {\n var ndims;\n var out;\n var i;\n \n // Determine the number of dimensions:\n ndims = means.length;\n \n // For each dimension, generate a value corrupted by Guassian noise...\n out = [];\n for ( i = 0; i < ndims; i++ ) {\n out.push( randn( means[ i ], sigmas[ i ] ) );\n }\n // Return the noisy data:\n return out;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":264,"value":"md`\nNext, we define a function which returns a discrete-time hidden Markov chain simulator as a JavaScript iterator\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":36,"value":"$33","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":268,"value":"md`\nWe can now define Markov chain properties. We'll start by defining the set of initial state probabilities\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"I = [ 0.1, 0.3, 0.2, 0.1, 0.3 ] // should sum to 1","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":271,"value":"md`\nNext, we define the state transition matrix which specifies the probability of transitioning from state ${tex`i`.outerHTML} to state ${tex`j`.outerHTML}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"A = {\n var transition = new Array( 5 );\n \n // Transition probabilities when in state s_0:\n transition[ 0 ] = [ 0.2, 0.7, 0.1, 0.0, 0.0 ]; // should sum to 1\n \n // Transition probabilities when in state s_1:\n transition[ 1 ] = [ 0.4, 0.3, 0.25, 0.05, 0.0 ]; // should sum to 1\n \n // Transition probabilities when in state s_2:\n transition[ 2 ] = [ 0.05, 0.2, 0.4, 0.3, 0.05 ]; // should sum to 1\n \n // Transition probabilities when in state s_3:\n transition[ 3 ] = [ 0.02, 0.18, 0.2, 0.2, 0.4 ]; // should sum to 1\n \n // Transition probabilities when in state s_4:\n transition[ 4 ] = [ 0.3, 0.0, 0.0, 0.2, 0.5 ]; // should sum to 1\n \n return transition;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":274,"value":"md`\nTo map states to observed values, we define state observation means (i.e., the average observed value for a given state)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"means = [ [ 0.2, 0.7 ], [ 0.35, 0.52 ], [ 0.55, 0.67 ], [ 0.6, 0.1 ], [ 0.8, 0.1 ] ]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":277,"value":"md`\nTo simulate state noise, we define state observation standard deviations\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"sigmas = [ [ 0.09, 0.05 ], [ 0.11, 0.07 ], [ 0.07, 0.08 ], [ 0.12, 0.04 ], [ 0.15, 0.04 ] ]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":341,"value":"md`\nFinally, we define convenience variables for the number of simulated states and dimensions\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"nStates = means.length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":107,"value":"ndims = means[ 0 ].length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":280,"value":"md`\nTo demonstate that the simulator works, we can simulate a few data points...\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":61,"value":"it = yield simulator( 10, I, A, means, sigmas, 123456 )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"it","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":283,"value":"md`\nNow that our simulator is generating data, let's generate data for subsequent clustering.\n\nWe begin by defining the number of data points to generate\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":390,"value":"N = 2500","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":394,"value":"md`\nand then incrementally generate simulated data\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":72,"value":"sample_data = {\n var states;\n var seed;\n var it;\n var x;\n var y;\n var v;\n \n // Define a seed in order to ensure that simulated data is easily reproducible:\n seed = 123456;\n \n // Create a new (seeded) simulator:\n it = simulator( N, I, A, means, sigmas, seed );\n \n // Initialize output arrays for storing the simulated values:\n x = [];\n y = [];\n states = [];\n \n // Generate simulated data...\n while ( true ) {\n v = it.next();\n if ( v.done ) {\n break;\n }\n // Note: we assume 2-dimensional data...\n x.push( v.value[ 0 ] );\n y.push( v.value[ 1 ] );\n states.push( v.value[ 2 ] );\n }\n return [ x, y, states ];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":419,"value":"md`\nTo visualize the evolution of the simulated system, we can generate a [plot](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/plot)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":421,"value":"sample_timeseries_plot = {\n var x = [];\n var i;\n \n for ( i = 0; i < N; i++ ) {\n x.push( i ); \n }\n return plot( [ x, x ], [ sample_data[ 0 ], sample_data[ 1 ] ], {\n 'xMin': 0,\n 'xMax': 100, // adjust to visualize more or less of the timeseries\n 'yMin': -0.1,\n 'yMax': 1.1,\n 'width': 800,\n 'height': 600\n });\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":426,"value":"html`${sample_timeseries_plot.render( 'html' )}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":347,"value":"md`\nTo visualize our simulated data as a two-dimensional scatter plot, we can generate another [plot](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/plot)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":75,"value":"sample_plot = plot( [ sample_data[ 0 ] ], [ sample_data[ 1 ] ], {\n 'xMin': -0.1,\n 'xMax': 1.1,\n 'yMin': -0.1,\n 'yMax': 1.1,\n 'lineStyle': 'none',\n 'symbols': 'closed-circle',\n 'symbolsOpacity': 0.15,\n 'width': 600,\n 'height': 600\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":77,"value":"html`${sample_plot.render( 'html' )}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":286,"value":"md`\nBased on the two-dimensional scatter plot, the data appears to be comprised of two large blobs with some possible structure within those larger blobs.\n\nTo see the underlying clusters, let's color code the data according to the underlying state which generated the data\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":102,"value":"sample_state_data = {\n var states;\n var X;\n var Y;\n var N;\n var s;\n var x;\n var y;\n var i;\n \n X = sample_data[ 0 ];\n Y = sample_data[ 1 ];\n states = sample_data[ 2 ];\n N = X.length;\n \n x = new Array( nStates );\n y = new Array( nStates );\n for ( i = 0; i < nStates; i++ ) {\n x[ i ] = [];\n y[ i ] = [];\n }\n // Group simulated data according to the state index...\n for ( i = 0; i < N; i++ ) {\n s = states[ i ];\n x[ s ].push( X[ i ] );\n y[ s ].push( Y[ i ] );\n }\n return [ x, y ];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":355,"value":"md`\nTo visualize the color-coded data, we can generate a new [plot](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/plot)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":120,"value":"sample_plot_color_coded = plot( sample_state_data[ 0 ], sample_state_data[ 1 ], {\n 'xMin': -0.1,\n 'xMax': 1.1,\n 'yMin': -0.1,\n 'yMax': 1.1,\n 'lineStyle': 'none',\n 'symbols': 'closed-circle',\n 'symbolsOpacity': 0.15,\n 'width': 600,\n 'height': 600\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":122,"value":"html`${sample_plot_color_coded.render( 'html' )}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":293,"value":"md`\nThat's better. We can see that the underlying clusters overlap. Our goal is to recover the underlying cluster centers (i.e., centroids).\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":296,"value":"md`\n* * *\n\n## Clustering\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":299,"value":"md`\nTo cluster the simulated data, we must first initialize an [incremental k-means cluster accumulator](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/ml/incr/kmeans)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"cluster = incrkmeans( nStates, ndims, {\n 'metric': 'euclidean',\n 'init': [ 'kmeans++' ],\n 'seed': 1234 // provide seed in order to ensure reproducible k-means++ initialization\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":302,"value":"md`\nOnce initialized, we can cluster simulated data as the data is generated\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":138,"value":"$34","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":305,"value":"md`\nTo plot the simulated data and detected cluster centers, we create another [plot](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/plot) instance\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"cluster_plot = plot({\n 'xMin': -0.1,\n 'xMax': 1.1,\n 'yMin': -0.1,\n 'yMax': 1.1,\n 'lineStyle': 'none',\n 'symbols': 'closed-circle',\n 'symbolsOpacity': [ 0.15, 0.01 ],\n 'width': 600,\n 'height': 600\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":197,"value":"cluster_plot_html = {\n cluster_plot.x = cluster_data[ 0 ];\n cluster_plot.y = cluster_data[ 1 ];\n return cluster_plot.render( 'html' );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":136,"value":"html`${cluster_plot_html}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":308,"value":"md`\nWe can see that, as more data is provided to the [incremental k-means algorithm](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/ml/incr/kmeans), the algorithm better learns the underlying structure of the generated data, recovering, to a reasonable approximation, the underlying states.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":433,"value":"md`\n* * *\n\n## Real-time Clustering\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":441,"value":"md`\nTo demonstrate the performance of [incremental k-means clustering](https://github.com/stdlib-js/stdlib/tree/2d6f6e67a8c66932f90422716c7a0ef5e6d53e4c/lib/node_modules/%40stdlib/ml/incr/kmeans), we can run a dynamic simulation.\n\nIn order to support interrupting and re-running a simulation, we'll first define a class for encapsulating cluster analysis and plot rendering\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":462,"value":"$35","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":540,"value":"md`\nNow that we have a mechanism for managing cluster analysis, we can create a new analyzer\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":496,"value":"analyzer = new Analyzer()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":533,"value":"md`\nIn order to simulate \"real-time\" analysis, we'll define logic for generating a simulated datum after a specified time interval\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":438,"value":"simulated_datum = {\n var simulate;\n var interval;\n var seed;\n var v;\n \n // Define a seed in order to ensure that simulated data is easily reproducible:\n seed = 123456;\n \n // Define the interval between simulated datums:\n interval = 100; // milliseconds\n \n // Create a new simulator:\n simulate = simulator( 0, I, A, means, sigmas, seed ); // ATTN: uncomment me to clear the simulation!\n //simulate = simulator( N, I, A, means, sigmas, seed ); // ATTN: uncomment me to start the simulation!\n \n // Reset the simulation:\n yield Promises.delay( interval, null );\n \n // Simulate real-time data...\n while ( true ) {\n v = simulate.next();\n if ( v.done ) {\n yield Promises.delay( interval, null );\n break;\n }\n yield Promises.delay( interval, v.value.slice( 0, ndims ) );\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":567,"value":"md`\n**NOTE**: you'll need to edit the above code block by commenting and uncommenting source lines in order for the simulation to run.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":545,"value":"md`\nWe next need to define some logic for updating cluster analysis upon receiving a new datum\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":449,"value":"analysis_plots = {\n if ( simulated_datum === null ) {\n analyzer.init();\n return analyzer.render();\n }\n analyzer.update( simulated_datum );\n return analyzer.render();\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":548,"value":"md`\nAnd, finally, we render the plots to see clustering happen in real-time!\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":508,"value":"html`${analysis_plots[ 0 ]}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":511,"value":"html`${analysis_plots[ 1 ]}`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":436,"value":"md`\n* * *\n\n## Conclusion\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":414,"value":"md`\nIf you are interested in learning more about [stdlib](https://github.com/stdlib-js/stdlib), be sure to check out the GitHub [repository](https://github.com/stdlib-js/stdlib) and to follow updates on [Twitter](https://twitter.com/stdlibjs). :)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":410,"value":"md`\n* * *\n\n## License\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":412,"value":"md`\nCopyright (c) 2018 Athan Reines.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 32:"$31:body"